A description of the composite elastic modulus of multilayer coated systems

The evaluation of the elastic response of coated systems under indentation loading represents a crucial issue, which determines the behavior of such systems under tribological applications. Although a number of models have been proposed in the literature for the description of the change in the composite modulus with indentation depth, as well as for the determination of the elastic modulus of monolayer coatings, only few works address the analysis of multilayer coatings. The present work proposes a general methodology, which allows the modification and extension of the models employed in the analysis of monolayer coatings, for the study of the elastic response of multilayer coatings. For this purpose, a number of models have been examined, including those proposed by Gao et al., Menčík et al., Perriot and Barthel, Antunes et al., Korsunsky and Constantinescu, Doerner and Nix, Bec et al. and Bull. The foundation of the advanced formalism is the physically-based concept proposed by Iost et al. for the computation of the volume fraction of each layer in the coating and therefore, of its contribution to the global elastic response under indentation. The modified models are further employed in the analysis of a coated system composed of a 2024-T6 aluminum alloy substrate coated with a multilayer coating of DLC/CrC/CNiPCr/NiP of approximately 54 μm in thickness, as well as, a set of experimental data reported by Bull for a bilayer coated system. It has been shown that the different models analyzed are able to provide a satisfactory description of the experimental data, although the quality of the fit depends on the number of material parameters involved in each model. The mean square error of the fit is employed for conducting a comparison between the models.